Computational Physics Coursework: Electronic Structure of Graphene Nanoribbons in the Tight-Binding Model

This was my first of two coursework projects for my Computational Physics module, conducted in semester 2 of my 25/26 academic year. In this work, a 7 page limit (excluding references and appendices) was imposed. I followed a prescribed template, with the report uploaded here for the purposes of online documentation of my work so far.Abstract: In this article a computational study of the electronic properties of graphene nanoribbons using a nearest-neighbour tight-binding model is presented. The geometry of graphene nanoribbons comes in two distinct types: armchair and zigzag nanoribbons of varying width are constructed numerically and their Bloch Hamiltonians are diagonalised to obtain the band structure and density of states. The calculations reproduce the width-dependence in band gap behaviour of armchair nanoribbons, as well as the characteristic edge states of zigzag ribbons. Numerical convergence tests and recovery of the graphene Dirac dispersion serve to demonstrate the reliability of the computational approach. These results illustrate how tight-binding calculations can predict electronic behaviour of graphene nanostructures beyond what can be obtained analytically.